If the three numbers in the ratio 3 : 2 : 5 be such that the sum of the squares is equal to 1862 then which number is the middle one.Options16131514

The problem is asking for the middle number in a ratio of 3:2:5 where the sum of the squares of these numbers equals 1862.

Here are the steps to solve this problem:

1. Let's denote the three numbers as 3x, 2x, and 5x.

2. According to the problem, the sum of the squares of these numbers is 1862. So, we can write the equation as (3x)^2 + (2x)^2 + (5x)^2 = 1862.

3. Simplifying the equation gives 9x^2 + 4x^2 + 25x^2 = 1862.

4. Adding the like terms gives 38x^2 = 1862.

5. Solving for x^2, we get x^2 = 1862 / 38 = 49.

6. Taking the square root of both sides, we get x = 7.

7. The middle number in the ratio is 2x, so substituting x = 7, we get 2*7 = 14.

So, the middle number is 14.